% Drawing a graph
% Author: Stefan Kottwitz
% https://www.packtpub.com/hardware-and-creative/latex-cookbook
\documentclass[border=10pt]{standalone}
\usepackage{tkz-graph}
%\GraphInit[vstyle = Shade]
\tikzset{
  LabelStyle/.style = { rectangle, rounded corners, draw,
                        minimum width = 2em, fill = white!50,
                        text = black, font = \bfseries },
  VertexStyle/.append style = { inner sep=5pt,
                                font = \Large\bfseries},
  EdgeStyle/.append style = {->, bend left} }
\thispagestyle{empty}
\begin{document}
\begin{tikzpicture}
  \SetGraphUnit{5}
  \SetVertexMath
  \Vertices{circle}{x_1,x_2,x_3,x_4}
%  \Vertex{B}
 % \SO(B){A}
 % \EA(B){C}
  \Loop[dist = 4cm, dir = NOWE, label = $p_{11}$](x_1.west)
 \Edge[label = $p_{12}$](x_1)(x_2)
 \Edge[label = $p_{21}$](x_2)(x_1)
 \Edge[label = $p_{14}$](x_1)(x_4)
 \tikzset{EdgeStyle/.append style = {bend right}}
 \Edge[label = $p_{23}$](x_2)(x_3)
  \Edge[label = $p_{34}$](x_3)(x_4)
 \Edge[label = $p_{43}$](x_4)(x_3)
 \Loop[dist = 4cm, dir = SOEA, label = $p_{44}$](x_4.north)
%  \Loop[dist = 4cm, dir = NO, label = 5](A.west)
 % \Loop[dist = 4cm, dir = SO, label = 6](C.east)
 \tikzset{EdgeStyle/.append style = {bend left = 0}}
 \Edge[label = $p_{31}$](x_3)(x_1)
%  \Edge[label = 7](A)(C)
 % \Edge[label = 8](C)(A)
\end{tikzpicture}
\end{document}